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I have made an experimental work and I am ask to provide a formal experimental error analysis. I have a difficulty to choose the appropriate analysis way and would like to have some advices or explanations.

I have measured a temperatures at the intlet (Ti) and outlet (To) of a heat exchanger and the mass flow rate of the fluid. I can calculate the power:

Q = mC (To-Ti)

From what I learn on uncertainty calculations, I am a little bit confused. I finally found that I could calculate my uncertainty in two ways:

(1): [itex]\frac{ΔQ}{Q}[/itex] = [itex]\frac{Δm}{m}[/itex]+ [itex]\frac{2ΔT}{To-Ti}[/itex]

(2): [itex]\frac{ΔQ}{Q}[/itex] =[itex]\sqrt{\left(\frac{Δm}{m}\right)^2+\left(\frac{2ΔT}{To-Ti}\right)^2}[/itex]

Δm: accuracy of the mass flowrate meter (documentation of the supplier)

ΔT: accuracy of the mass flowrate meter (value given by the calibration center)

C is admit as a constant

I made just one measurement.

**Which one of the above equations must I use and why?**

Actually, I derived heat transfer coefficients (built a curve) from several measurements, by changing the flowrate m and the inlet temperature Ti. But no test has been repeated in the same conditions. Is the first method or the second one am I going to use for the "error analysis"?

Thank you in advance.

P.S.

**Please, even if you do not have a time, even a short answer would be useful for me.**